Is H a normal subgroup in G? [closed]
$begingroup$
Let $G = S_5$ and let $H = langle(1, 2, 3, 4, 5)rangle$. Is $H$ a normal subgroup of $G$ ?
Having some trouble figuring out this problem, it would be great if someone can help to find it!
group-theory normal-subgroups
edited Dec 3 '18 at 17:45
Chinnapparaj R
5,3131828
asked Dec 3 '18 at 16:17
jessicajessica
42
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closed as off-topic by Derek Holt, amWhy, Leucippus, KReiser, user10354138 Dec 4 '18 at 2:46
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Derek Holt, amWhy, Leucippus, KReiser, user10354138
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
Let $G = S_5$ and let $H = langle(1, 2, 3, 4, 5)rangle$. Is $H$ a normal subgroup of $G$ ?
Having some trouble figuring out this problem, it would be great if someone can help to find it!
group-theory normal-subgroups
edited Dec 3 '18 at 17:45
Chinnapparaj R
5,3131828
asked Dec 3 '18 at 16:17
jessicajessica
42
$endgroup$
closed as off-topic by Derek Holt, amWhy, Leucippus, KReiser, user10354138 Dec 4 '18 at 2:46
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Derek Holt, amWhy, Leucippus, KReiser, user10354138
If this question can be reworded to fit the rules in the help center, please edit the question.
3
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What would happen if you conjugate generator by any transposition?
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– Sunny Rathore
Dec 3 '18 at 16:18
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@ Sunny Rathore im not sure.I'm new to the group theory.
$endgroup$
– jessica
Dec 3 '18 at 16:38
$begingroup$
What are h and i in the problem statement? Are they just denoting brackets?
$endgroup$
– Chickenmancer
Dec 3 '18 at 16:49
$begingroup$
@Chickenmancer: that was by mistake, edited now.
$endgroup$
– jessica
Dec 3 '18 at 16:54
add a comment |
$begingroup$
Let $G = S_5$ and let $H = langle(1, 2, 3, 4, 5)rangle$. Is $H$ a normal subgroup of $G$ ?
Having some trouble figuring out this problem, it would be great if someone can help to find it!
group-theory normal-subgroups
edited Dec 3 '18 at 17:45
Chinnapparaj R
5,3131828
asked Dec 3 '18 at 16:17
jessicajessica
42
$endgroup$
Let $G = S_5$ and let $H = langle(1, 2, 3, 4, 5)rangle$. Is $H$ a normal subgroup of $G$ ?
Having some trouble figuring out this problem, it would be great if someone can help to find it!
group-theory normal-subgroups
group-theory normal-subgroups
edited Dec 3 '18 at 17:45
Chinnapparaj R
5,3131828
asked Dec 3 '18 at 16:17
jessicajessica
42
edited Dec 3 '18 at 17:45
Chinnapparaj R
5,3131828
asked Dec 3 '18 at 16:17
jessicajessica
42
edited Dec 3 '18 at 17:45
Chinnapparaj R
5,3131828
edited Dec 3 '18 at 17:45
Chinnapparaj R
5,3131828
edited Dec 3 '18 at 17:45
Chinnapparaj R
5,3131828
5,3131828
asked Dec 3 '18 at 16:17
jessicajessica
42
asked Dec 3 '18 at 16:17
jessicajessica
42
asked Dec 3 '18 at 16:17
jessicajessica
42
42
closed as off-topic by Derek Holt, amWhy, Leucippus, KReiser, user10354138 Dec 4 '18 at 2:46
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Derek Holt, amWhy, Leucippus, KReiser, user10354138
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Derek Holt, amWhy, Leucippus, KReiser, user10354138 Dec 4 '18 at 2:46
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Derek Holt, amWhy, Leucippus, KReiser, user10354138
If this question can be reworded to fit the rules in the help center, please edit the question.
3
$begingroup$
What would happen if you conjugate generator by any transposition?
$endgroup$
– Sunny Rathore
Dec 3 '18 at 16:18
$begingroup$
@ Sunny Rathore im not sure.I'm new to the group theory.
$endgroup$
– jessica
Dec 3 '18 at 16:38
$begingroup$
What are h and i in the problem statement? Are they just denoting brackets?
$endgroup$
– Chickenmancer
Dec 3 '18 at 16:49
$begingroup$
@Chickenmancer: that was by mistake, edited now.
$endgroup$
– jessica
Dec 3 '18 at 16:54
add a comment |
3
$begingroup$
What would happen if you conjugate generator by any transposition?
$endgroup$
– Sunny Rathore
Dec 3 '18 at 16:18
$begingroup$
@ Sunny Rathore im not sure.I'm new to the group theory.
$endgroup$
– jessica
Dec 3 '18 at 16:38
$begingroup$
What are h and i in the problem statement? Are they just denoting brackets?
$endgroup$
– Chickenmancer
Dec 3 '18 at 16:49
$begingroup$
@Chickenmancer: that was by mistake, edited now.
$endgroup$
– jessica
Dec 3 '18 at 16:54
3
3
$begingroup$
What would happen if you conjugate generator by any transposition?
$endgroup$
– Sunny Rathore
Dec 3 '18 at 16:18
$begingroup$
What would happen if you conjugate generator by any transposition?
$endgroup$
– Sunny Rathore
Dec 3 '18 at 16:18
$begingroup$
@ Sunny Rathore im not sure.I'm new to the group theory.
$endgroup$
– jessica
Dec 3 '18 at 16:38
$begingroup$
@ Sunny Rathore im not sure.I'm new to the group theory.
$endgroup$
– jessica
Dec 3 '18 at 16:38
$begingroup$
What are h and i in the problem statement? Are they just denoting brackets?
$endgroup$
– Chickenmancer
Dec 3 '18 at 16:49
$begingroup$
What are h and i in the problem statement? Are they just denoting brackets?
$endgroup$
– Chickenmancer
Dec 3 '18 at 16:49
$begingroup$
@Chickenmancer: that was by mistake, edited now.
$endgroup$
– jessica
Dec 3 '18 at 16:54
$begingroup$
@Chickenmancer: that was by mistake, edited now.
$endgroup$
– jessica
Dec 3 '18 at 16:54
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Consider $(12)(12345)(12)=(13452)notinlangle (12345)rangle ={e,(12345),(13524),(14253),(15432)}$.
answered Dec 3 '18 at 16:47
Chris CusterChris Custer
11.3k3824
$endgroup$
add a comment |
$begingroup$
Chris Custer provides an answer by using definition but I hope the following is useful to you for finding normal subgroups in $S_n$
Hint: A subgroup $H$ of $G$ is normal $iff$ $H$ is the union of conjugacy classes
$$&$$ Remember that, elements of $S_n$ are conjugate $iff$ they have the same cycle type
answered Dec 3 '18 at 18:31
Chinnapparaj RChinnapparaj R
5,3131828
$endgroup$
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Consider $(12)(12345)(12)=(13452)notinlangle (12345)rangle ={e,(12345),(13524),(14253),(15432)}$.
answered Dec 3 '18 at 16:47
Chris CusterChris Custer
11.3k3824
$endgroup$
add a comment |
$begingroup$
Consider $(12)(12345)(12)=(13452)notinlangle (12345)rangle ={e,(12345),(13524),(14253),(15432)}$.
answered Dec 3 '18 at 16:47
Chris CusterChris Custer
11.3k3824
$endgroup$
add a comment |
$begingroup$
Consider $(12)(12345)(12)=(13452)notinlangle (12345)rangle ={e,(12345),(13524),(14253),(15432)}$.
answered Dec 3 '18 at 16:47
Chris CusterChris Custer
11.3k3824
$endgroup$
Consider $(12)(12345)(12)=(13452)notinlangle (12345)rangle ={e,(12345),(13524),(14253),(15432)}$.
answered Dec 3 '18 at 16:47
Chris CusterChris Custer
11.3k3824
answered Dec 3 '18 at 16:47
Chris CusterChris Custer
11.3k3824
answered Dec 3 '18 at 16:47
Chris CusterChris Custer
11.3k3824
answered Dec 3 '18 at 16:47
Chris CusterChris Custer
11.3k3824
11.3k3824
add a comment |
add a comment |
$begingroup$
Chris Custer provides an answer by using definition but I hope the following is useful to you for finding normal subgroups in $S_n$
Hint: A subgroup $H$ of $G$ is normal $iff$ $H$ is the union of conjugacy classes
$$&$$ Remember that, elements of $S_n$ are conjugate $iff$ they have the same cycle type
answered Dec 3 '18 at 18:31
Chinnapparaj RChinnapparaj R
5,3131828
$endgroup$
add a comment |
$begingroup$
Chris Custer provides an answer by using definition but I hope the following is useful to you for finding normal subgroups in $S_n$
Hint: A subgroup $H$ of $G$ is normal $iff$ $H$ is the union of conjugacy classes
$$&$$ Remember that, elements of $S_n$ are conjugate $iff$ they have the same cycle type
answered Dec 3 '18 at 18:31
Chinnapparaj RChinnapparaj R
5,3131828
$endgroup$
add a comment |
$begingroup$
Chris Custer provides an answer by using definition but I hope the following is useful to you for finding normal subgroups in $S_n$
Hint: A subgroup $H$ of $G$ is normal $iff$ $H$ is the union of conjugacy classes
$$&$$ Remember that, elements of $S_n$ are conjugate $iff$ they have the same cycle type
answered Dec 3 '18 at 18:31
Chinnapparaj RChinnapparaj R
5,3131828
$endgroup$
Chris Custer provides an answer by using definition but I hope the following is useful to you for finding normal subgroups in $S_n$
Hint: A subgroup $H$ of $G$ is normal $iff$ $H$ is the union of conjugacy classes
$$&$$ Remember that, elements of $S_n$ are conjugate $iff$ they have the same cycle type
answered Dec 3 '18 at 18:31
Chinnapparaj RChinnapparaj R
5,3131828
answered Dec 3 '18 at 18:31
Chinnapparaj RChinnapparaj R
5,3131828
answered Dec 3 '18 at 18:31
Chinnapparaj RChinnapparaj R
5,3131828
answered Dec 3 '18 at 18:31
Chinnapparaj RChinnapparaj R
5,3131828
5,3131828
add a comment |
add a comment |
3
$begingroup$
What would happen if you conjugate generator by any transposition?
$endgroup$
– Sunny Rathore
Dec 3 '18 at 16:18
$begingroup$
@ Sunny Rathore im not sure.I'm new to the group theory.
$endgroup$
– jessica
Dec 3 '18 at 16:38
$begingroup$
What are h and i in the problem statement? Are they just denoting brackets?
$endgroup$
– Chickenmancer
Dec 3 '18 at 16:49
$begingroup$
@Chickenmancer: that was by mistake, edited now.
$endgroup$
– jessica
Dec 3 '18 at 16:54